The Application Of Smoothing Estimation Methods In Semi-parametric Survival Models

Recently, the collection of patient's survival data in biomedical field has been gradually developed, which provides more convenience for researchers. The re-search of survival analysis has been expanded and deepen. Some new survival models based on real data sets have been proposed, such as accelerated hazard model and mixture cure rate models, etc. Based on these new models, researchers have proposed and developed corresponding new estimation methods. In the re-cent decade, the smoothing problem of semi-parametric survival models has been improved, which makes these new models used widely in practice.In this dissertation, we focus on discussing several important semi-parametric survival models and the application of three different smoothing estimation meth-ods, which have been proposed and developed in recent decade. Firstly, there is an introduction in Chapter1, which includes the research background and the main work of this dissertation. In Chapter2, two classes of semi-parametric survival models which we are interested in are introduced:the hazard regression models and the mixture cure rate models. In Chapter3, we introduce several widely used estimation methods for semi-parametric survival models. The main part of this dissertation contains three different smoothing estimation methods. In Chapter4, an induced smoothing estimation method based on rank-type estimation equation is applied to accelerated hazard model. In Chapter5, a profile likelihood function method is applied in the EM algorithm of accelerated hazard mixture cure rate model. In Chapter6, we propose that a smooth semi-nonparametric estimation method can be applied to the mixture cure rate models. We also investigate the performance and reliability of each method through simulation and comparison study. In Chapter7, we analysis three real data sets of breast cancer patients and investigate the effects of different stages on the cure rates and the survival distribution of uncured patients. Finally, a summary and research direction of the future are in Chapter8.In this dissertation, we have several points of innovation, which are:(1) successfully apply the induced smoothing estimation method to acceler-ated hazard model, and make the estimation of parameters and their variances better and more reliable.(2) successfully apply the profile likelihood function method in the EM al-gorithm of accelerated hazard mixture cure rate model, and solve the problem of obtaining smoothed estimation of survival function.(3) propose a new smooth semi-nonparametric estimation method for mixture cure rate models, which can make the estimation of parameters and variances easier via a smooth representation of survival density.(4) successfully analysis the survival data in breast cancer by semi-parametric mixture cure rate models using different smoothing methods, obtain the estima-tion of survival distribution and cure rate in different breast cancer stages, and provide evidence of predicting survival time of patients by reliable estimation of parameters'variances.